Transient Analysis MCQ [Free PDF] – 6 Objective Questions with Answers

A first-order RC charging circuit responds exponentially because the capacitor voltage cannot change instantaneously. The time constant τ=RC sets the speed; at t=τ the capacitor reaches about 63.2% of its final voltage. Key relation: v_C(t)=V(1−e^(−t/RC)); i(t)=(V/R)e^(−t/RC); τ=RC.

Exam focus: One time constant = 63.2%; five time constants ≈ settled. Common trap: Charging current decreases with time; it does not increase toward steady state.

In a first-order RL circuit driven by a DC step, inductor current cannot change instantaneously. The time constant depends on both inductance and resistance, so changing either alters the transient speed. Key relation: i(t)=V/R·(1−e^(−t/τ)); τ=L/R.

Exam focus: Initial inductor current is continuous; final DC inductor acts as a short circuit. Common trap: Do not write τ=L alone; resistance is part of the time constant.

For an RL switching response i(t)=I∞+(I0+−I∞)e⁻ᵗ/τ, the given expression identifies I∞=2.5 A, the initial current as 4 A, and τ=1/4 s. Applying the pre-switch and post-switch DC equivalents and τ=L/Req gives R1=3 Ω and R2=5 Ω.

For an RL circuit the time constant is τ=L/R. It increases when inductance increases and when resistance decreases, because larger L resists current change while larger R dissipates energy faster.

Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. An underdamped response oscillates with exponentially decaying amplitude, critical damping gives the fastest non-oscillatory response, and overdamping gives a slower non-oscillatory response. Key relation: Characteristic form: s²+2ζω_n s+ω_n²=0.

Exam focus: ζ1 overdamped. Common trap: Overdamped responses do not sustain oscillations.

Damping is determined from the homogeneous second-order equation, not from the forcing term. Comparing s² + s + 1 with s² + 2ζωₙs + ωₙ² gives ωₙ = 1 rad/s and ζ = 0.5. Since 0 < ζ < 1, the series RLC response is underdamped and its natural response decays while oscillating.